On the Satisfiability of Quasi-Classical Description Logics

Though quasi-classical description logic (QCDL) can tolerate the inconsistency of description logic in reasoning, a knowledge base in QCDL possibly has no model. In this paper, we investigate the satisfiability of QCDL, namely, QC-coherency and QC-consistency and develop a tableau calculus, as a formal proof, to determine whether a knowledge base in QCDL is QC-consistent. To do so, we repair the standard tableau for DL by introducing several new expansion rules and defining a new closeness condition. Finally, we prove that this calculus is sound and complete. Based on this calculus, we implement an OWL paraconsistent reasoner called QC-OWL. Preliminary experiments show that QC-OWL is highly efficient in checking QC-consistency

Verifying Real-Time Systems using Explicit-time Description Methods

Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems with general untimed model checkers. Lamport presented an explicit-time description method using a clock-ticking process (Tick) to simulate the passage of time together with a group of global variables for time requirements. This paper proposes a new explicit-time description method with no reliance on global variables. Instead, it uses rendezvous synchronization steps between the Tick process and each system process to simulate time. This new method achieves better modularity and facilitates usage of more complex timing constraints. The two explicit-time description methods are implemented in DIVINE, a well-known distributed-memory model checker. Preliminary experiment results show that our new method, with better modularity, is comparable to Lamport's method with respect to time and memory efficiency

Relational Proof System for Linear and Other Substructural Logics

In this paper we give relational semantics and an accompanying relational proof system for a variety of intuitionistic substructural logics, including (intuitionistic) linear logic with exponentials. Starting with the (Kripke-style) semantics for FL as discussed in [13], we developed, in [11], a relational semantics and a relational proof system for full Lambek calculus. Here, we take this as a base and extend the results to deal with the various structural rules of exchange, contraction, weakening and expansion, and also to deal with an involution operator and with the operators ! and ? of linear logic. To accomplish this, for each extension X of FL we develop a Kripke-style semantics, RelKripke X semantics, as a bridge to relational semantics. The RelKripke X semantics consists of a set with distinguished elements, ternary relations and a list of conditions on the relations. For each extension X, RelKripke X semantics is accompanied by a Kripke-style valuation system analogous to th..

Logical and sheaf theoretic methods in the study of geometric fields in sheaf toposes over Boolean spaces and applications to Von Neumann regular rings

We investigate some properties of (geometric) fields in toposes of sheaves over Boolean spaces and establish the internal validity of a number of classical theorems from Algebraic Geometry and the theory of ordered fields. We then use our results to obtain, via sheaf representations, some know theorems about (von Neumann) regular rings as well as some new theorems for regular f-rings. By contrast with previous investigations in these last two subjects (Saracino and Weispfenning {39} and van den Dries {42}) a more natural approach, inspired by work of Macintyre {30}, Loullis {29}, Bunge-Reyes {7} and Bunge {4},{5} is employed here. In addition to sheaf theoretic methods we use a variety of logical methods from geometric logic, infinitary intuitionistic logic and model theory. We also prove some new theorems on the transfer of subobjects along certain morphisms and a "lifting theorem" taking truth from statements about global sections to their internal validity

CTL Model-Checking over Logics with Non-Classical Negations

In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to reasoning over these logics